An Upper Bound on the Capacity of Bandlimited LTI AWGN Channels Subject to Peak-Amplitude Constraint

In this paper we consider the upper bound on the capacity of bandlimited linear, time-invariant (LTI) channels with additive white Gaussian noise (AWGN) in which the input signal is subject to a peak amplitude constraint. It has been shown that when the channel impulse response (CIR) is square-integrable, unit processes attain the largest achievable rate for this channel, [Ozarow et al., 1988], yet the characterization of such processes is associated with a high numerical complexity. In this work we use a characterization of the autocorrelation function for unit processes derived in [Quintanilla, 2008], which facilitates a simpler and structured numerical evaluation of necessary condition for the autocorrelation function of unit processes, originally characterized in [Mcmillan, 1955] and [Shepp, 1967]. We translate this characterization into spectral constraints on the input power spectral density (PSD), following the approach applied in [Shamai and Bar-David, 1989], to tighten their bound on the capacity of such channels.